A Nonlocal Kronecker-Basis-Representation Method for Low-Dose CT Sinogram Recovery (Journal of Computational Mathematics, 2024)
Low-dose computed tomography (LDCT) contains the mixed noise of Poisson and Gaussian, which makes the image reconstruction a challenging task. In order to describe thestatistical characteristics of the mixed noise, we adopt the sinogram preprocessing as a standard maximum a posteriori (MAP). Based on the fact that the sinogram of LDCT has nonlocal self-similarity property, it exhibits low-rank characteristics. The conventional way ofsolving the low-rank problem is implemented in matrix forms, and ignores the correlationsamong similar patch groups. To avoid this issue, we make use of a nonlocal Kronecker-Basis-Representation (KBR) method to depict the low-rank problem. A new denoisingmodel, which consists of the sinogram preprocessing for data fidelity and the nonlocalKBR term, is developed in this work. The proposed denoising model can better illustratethe generative mechanism of the mixed noise and the prior knowledge of the LDCT. Numerical results show that the proposed denoising model outperforms the state-of-the-artalgorithms in terms of peak-signal-to-noise ratio (PSNR), feature similarity (FSIM), andnormalized mean square error (NMSE).
Keywords: Low-dose computed tomography; Kronecker-basis-representation; Low-rank approximation; Noise-generating-mechanism.